Zeno's Paradoxes

Zeno's paradoxes are a series of philosophical arguments devised by the ancient Greek philosopher Zeno of Elea in support of his teacher Parmenides's monism, the view that despite ordinary sensory experience, reality is single and unchanging. Known today mainly through the accounts of Plato, Aristotle and later commentators such as Simplicius, the paradoxes challenge the coherence of plurality, motion, space and time by arguing that each leads to logical contradiction. Of Zeno's reported forty paradoxes of plurality and several arguments against motion, only a few survive in detail, most famously the Achilles paradox, in which a swift runner can never overtake a slower tortoise given a head start because the gap between them can always be infinitely subdivided, seemingly requiring an infinite number of steps to close it. The paradoxes have driven extensive philosophical and mathematical debate about infinity and continuity ever since, from Aristotle's early distinction between potential and actual infinity to the later resolution offered by the mathematics of calculus.